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Research ArticleDigital Image Steganography Using LSB SubstitutionPVD and EMD

Anita Pradhan K Raja Sekhar and Gandharba Swain

Department of Computer Science and Engineering Koneru Lakshmaiah Education Foundation VaddeswaramAndhra Pradesh 522502 India

Correspondence should be addressed to Gandharba Swain gswain1234gmailcom

Received 29 March 2017 Revised 14 July 2017 Accepted 25 July 2017 Published 5 September 2018

Academic Editor Julien Bruchon

Copyright copy 2018 Anita Pradhan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To protect from pixel difference histogram (PDH) analysis and RS analysis two hybrid image steganography techniques byappropriate combination of LSB substitution pixel value differencing (PVD) and exploiting modification directions (EMD) havebeen proposed in this paper The cover image is traversed in raster scan order and partitioned into blocks The first techniqueoperates on 2 times 2 pixel blocks and the second technique operates on 3 times 3 pixel blocks For each block the average pixel valuedifference 119889 is calculated If 119889 value is greater than 15 the block is in an edge area so a combination of LSB substitution and PVDis applied If 119889 value is less than or equal to 15 the block is in a smooth area so a combination of LSB substitution and EMD isapplied Each of these two techniques exists in two variants (Type 1 andType 2) with respect to two different range tablesThe hidingcapacities and PSNR of both the techniques are found to be improved The results from experiments prove that PDH analysis andRS analysis cannot detect these proposed techniques

1 Introduction

The fundamental principle of a steganography technique isto hide the secret data in image audio or video files [1] Datacan be hidden in images using spatial domain or frequencydomain LSB substitution is the most common technique ofdata hiding in spatial domain But it can be easily detectedby RS analysis [2] To augment security in LSB substitutiontechniques some precautionary measures need to be takenThe LSB planes that will carry the secret data can be selectedbased upon the bit pattern hidden in neighboring pixels [3]The bits from one or more LSB planes of the pixels canbe joined together to make an array The binary data bitscan be concealed in this array at appropriate portions tominimize distortion and to improve the security [4] ThePVDsteganography is another familiar data hiding technique[5] This technique exploits the smooth areas to hide lessernumber of secret bits and edge areas to hide more number ofsecret bits Many variants of PVD technique have been foundin literature A technique of Khodaei and Faez uses both LSBand PVD concepts [6] It possesses higher hiding capacityand lesser distortion The problem in the PVD techniques is

that they are attacked by pixel difference histogram (PDH)analysis One mechanism that addresses this problem is theadaptive range table [7 8] Instead of a fixed range table forall the pixels it can be varied for every pixel Even the numberof LSB bits to be hidden in different pixels can be varied basedon the smoothness of the block into which the pixel belongsto [9] so that security can be improved

Zhang and Wang [10] proposed exploiting modificationdirection (EMD) steganography The principal goal in it isthat a group of secret bits be converted to a digit in (2119899 + 1)-ary notational system where 119899 is the size of pixel block Thissecret digit could be hidden in the pixel block by adding plusmn1to only one pixel In this technique the hiding capacity isnot good The hiding capacity has been improved in two-stage technique in [11] and 8-ary technique in [12] Lee et al[13] proposed EMD technique using pixel segmentation Ina pair of pixels each pixel is segmented into two segmentsThe MSB segments of the two pixels together is called thevector of coordinates (VCA) and the LSB segments of the twopixels together are called vector modification area (VMA)The bits of VCA decide about embedding Jung and Yoo[14] proposed an EMD technique in a block of one pixel to

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 1804953 11 pageshttpsdoiorg10115520181804953

2 Mathematical Problems in Engineering

Pc P1

P2 P3

(a)

pc p

1

p2 p

3

(b)

plowastc plowast

1

plowast2 plowast

3

(c)

Figure 1 (a) Cover pixel block (b) stego block and (c) stego block used for extraction

increase the hiding capacity The EMD technique based ondiamond encoding also could improve the hiding capacity[15] Joo et alrsquos EMD technique using modulus functionpreserved the pixel difference histogram [16] Kim et al [17]has proposed two EMD techniques namely EMD-2 and 2-EMD In EMD-2 technique at most two pixels are modifiedand in 2-EMD technique two consecutive EMDs are usedBoth these techniques achieve higher hiding capacity Wanget al [18] said that a number of pixel groups could becombined to derive more number of embedding directionsso that distortion can be reduced Kieu and Changrsquos [19]EMD technique used eight modification directions It fullyexploited allmodification directions andmeasured the hidingcapacity and distortion for different values of the parameter 119904Wang et alrsquos [20] EMD technique combined multiple groupsto hide the data according to a designed switch map sothat the hiding capacity can be increased and distortioncan be decreased Fu et al [21] used EMD and multilayerembedding mechanism with histogram shifting to achievereversibility Kim [22] advanced the EMD technique usingbasis vector and (2119899+119909 minus 1)-ary notational system where119899 and 119909 are user defined values Shen and Huang [23]made the hiding capacity of a block adaptive by using PVDwith EMD This PVD with EMD technique provides higherhiding capacity and better PSNR To improve upon thesecurity keys are used to generate pseudo random num-bers which can be used to find the embedding locations[24]

It is found that Shen and Huangrsquos [23] PVD with EMDtechnique is detectable by PDH analysis To advance furtherin this paper we judiciously combined LSB substitution PVDand EMD techniques to protect against PDH analysis and topossess larger hiding capacity without sacrificing the PSNRThere are two techniques proposed the first technique isdesigned using 2 times 2 pixel blocks and the second techniqueis designed using 3 times 3 pixel blocks

2 The Proposed Technique 1 (LSB + PVD +EMD in 2 times 2 Pixel Blocks)

21 The Embedding Procedure

Step 1 The image is traversed in raster scan order andpartitioned into nonoverlapping blocks of size 2times 2 A sampleblock is shown in Figure 1(a)

Step 2 For every block the average pixel value difference 119889 =(13)sum3

119894=1|119875119888 minus 119875119894| is computed If 119889 is greater than 15 then

Table 1 Range table (Type 1)

Range119897119894 1199061198941198771 =0 71198772=

8 151198773=

16 311198774=

32 631198775=

64 1271198776=

128 255No of bitsto behidden 119899

119894

3 3 3 3 4 4

Table 2 Range table (Type 2)

Range119897119894 1199061198941198771 =0 71198772=

8 151198773=

16 311198774=

32 631198775=

64 1271198776=

128 255No of bitsto behidden 119899

119894

3 3 4 5 6 6

the block is said to be an edge area otherwise it is a smootharea

Step 3 In an edge area embedding is done using LSBsubstitution and PVD

Step 4 In a smooth area embedding is done using LSBsubstitution and EMD

TheLSB + PVDEmbedding Approach The first LSB of pixel119875119888is substituted by bit 1 to act as an indicator during extractionThe other 2 LSBs are substituted by 2 data bits A new valueof this pixel 1199011015840

119888is obtained Suppose the decimal value of the

three LSBs of 1199011015840119888is 1199041 and the decimal value of the three LSBs

of 119875119888 is 1198941 A difference value df1 = 1198941 minus 1199041 is calculated and 1199011015840119888

is optimized by

1199011015840119888=

1199011015840119888+ 23 if df1 gt 23minus1 0 le (1199011015840119888 + 23) le 2551199011015840119888minus 23 if df1 lt minus23minus1 0 le (1199011015840119888 minus 23) le 2551199011015840119888 otherwise

(1)

Now calculate three difference values 119889119894 = |1199011015840119888 minus 119901119894| for 119894 =1 2 3 It falls into one of the ranges in range table Based onthe range of 119889119894 the number of bits to be hidden (119899119894) can bedecided Table 1 can be referred to as Type 1 and Table 2 can bereferred to as Type 2 Now convert each 119899119894 bits of confidentialdata to its decimal value 119889119904119894 for 119894 = 1 2 3 Then compute thenew value for this difference as 1198891015840

119894= 119897119894 + 119889119904119894 for 119894 = 1 2 3

Now for each 119901119894 where 119894 = 1 2 3 calculate two new values

Mathematical Problems in Engineering 3

11990110158401015840119894= 1199011015840119888minus1198891015840119894and 119901101584010158401015840

119894= 1199011015840119888+1198891015840119894 Select one of these two values

as 1199011015840119894by applying

1199011015840119894=

11990110158401015840119894 if 10038161003816100381610038161003816119901119894 minus 119901

10158401015840

119894

10038161003816100381610038161003816 lt10038161003816100381610038161003816119901119894 minus 119901

101584010158401015840

119894

10038161003816100381610038161003816 0 le 11990110158401015840

119894le 255

119901101584010158401015840119894 otherwise

(2)

The LSB + EMD Embedding Approach The first LSB bit ofpixel 119901119888 is substituted by bit 0 which can act as an indicatorduring extraction The other two LSBs of 119901119888 are substituted bytwo data bits Thus a new value 1199011015840

119888of the pixel 119901119888 is obtained

Suppose the decimal value of the three LSBs of 1199011015840119888is 1199041 and

the decimal value of the three LSBs of 119875119888 is 1198941 A difference

value df1 = 1198941 minus 1199041 is calculated and 1199011015840119888is optimized by

(1)Suppose we denote the remaining pixels (1199011 1199012 1199013) by

a name 119901119896 where 119896 = 1 2 3 Now apply EMD for each 119901119896as follows Each 119901119896 has to hide 2 bits of data The decimalequivalent of the two data bits is 119898119896 Now select 119909 fromminus3 minus2 minus1 0 and calculate 11990110158401015840

119896= 119901119896 + 119909 such that the

condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly select 119909 from

1 2 3 and calculate 119901101584010158401015840119896= 119901119896 + 119909 such that the condition

(119901101584010158401015840119896

mod 4 = 119898119896) satisfies If for all the three values in list1 2 3 the condition (119901101584010158401015840

119896mod 4 = 119898119896) does not satisfy

then set 119901101584010158401015840119896= minus10 Now calculate the stego value 1199011015840

119896for 119901119896

by (3)

1199011015840119896=

11990110158401015840119896 if (119901101584010158401015840

119896lt 0 or 119901101584010158401015840

119896gt 255) 0 le 11990110158401015840

119896le 255 or 0 le (11990110158401015840

119896 119901101584010158401015840119896) le 255 10038161003816100381610038161003816119901119896 minus 119901

10158401015840

119896

10038161003816100381610038161003816 le10038161003816100381610038161003816119901119896 minus 119901

101584010158401015840

119896

10038161003816100381610038161003816119901101584010158401015840119896 if (11990110158401015840

119896lt 0 or 11990110158401015840

119896gt 255) 0 le 119901101584010158401015840

119896le 255 or 0 le (11990110158401015840

119896 119901101584010158401015840119896) le 255 10038161003816100381610038161003816119901119896 minus 119901

101584010158401015840

119896

10038161003816100381610038161003816 le10038161003816100381610038161003816119901119896 minus 119901

10158401015840

119896

10038161003816100381610038161003816(3)

Thus Figure 1(b) represents the stego-pixel block

22 The Extraction Procedure

Step 1 The stego image is traversed in raster scan orderand partitioned into nonoverlapping blocks of size 2 times 2Figure 1(c) represents a sample 2 times 2 stego-pixel block

Step 2 The LSB bit of 119901lowast119888is checked if it is 1 then for

this block the extraction procedure of LSB + PVD approachis used as follows The next two LSBs of 119901lowast

119888are extracted

Furthermore the 119889lowast119894= |119901lowast119888minus119901lowast119894| and 119904lowast

119894= 119889lowast119894minus119897119894 for 119894 = 1 2 3

are calculated where 119889lowast119894belongs to the range 119877119894 and 119897119894 is the

lower bound of this range Now each of these 119904lowast119894is converted

to 119899119894 binary bits where 119899119894 is the value corresponding to thesame range 119877119894 of 119889lowast119894 Note that the same range table (Table 1or Table 2) which was used during embedding should be usedduring extraction

Step 3 If the LSB bit of 119901lowast119888is 0 then for this block the

extraction procedure of LSB + EMD is applied as followsThenext two LSBs of119901lowast

119888are extracted For all the remaining pixels

(119901lowast1 119901lowast2 119901lowast3) the decimal equivalent of the embedded bits119898119896

is calculated as119898119896 = 119901lowast119896 mod 4 for 119896 = 1 2 3 Now each 119898119896is converted to 2 binary bits

3 The Proposed Technique 2 (LSB + PVD +EMD in 3 times 3 Pixel Blocks)

31 The Embedding Procedure

Step 1 The image is traversed in raster scan order andpartitioned into nonoverlapping blocks of size 3times 3 A sampleblock is shown in Figure 2(a)

Step 2 An average pixel value difference 119889 = (18)sum8119894=1|119875119888 minus

119875119894| is calculated

Step 3 If 119889 value is greater than 15 then a combination of LSBsubstitution and PVD is applied

Step 4 If 119889 value is less than or equal to 15 then a combina-tion of LSB substitution and EMD is applied

The LSB + PVD Embedding Approach In the central pixel119875119888 3 LSBs are substituted by 3 data bits A new value of thecentral pixel is found Say it is 1199011015840

119888 In pixel 1199018 the first LSB

is substituted by bit 1 which will be used as indicator duringextraction procedureThe other two LSBs in it are substitutedby two data bits After substituting three LSBs suppose thenew value of pixel 1199018 is 11990110158408 The decimal value of the threeLSBs of 1199011015840

119888is 1199041 and the decimal value of three LSBs of 119875119888 is

1198941 Similarly the decimal value of three LSBs of 11990110158408is 1199042 and

the decimal value of three LSBs of 1199018 is 1198942 Now calculate thedifferences df1 and df2 as df1 = 1198941 minus 1199041 and df2 = 1198942 minus 1199042 Nowoptimize the values of1199011015840

119888and11990110158408using (1) and (4) respectively

11990110158408=

11990110158408+ 23 if df2 gt 23minus1 0 le (11990110158408 + 23) le 25511990110158408minus 23 if df2 lt minus23minus1 0 le (11990110158408 minus 23) le 25511990110158408 otherwise

(4)

Now calculate seven difference values 119889119894 = |1199011015840119888 minus 119901119894| for119894 = 1 2 7 These difference values lie in one of the rangesof the range table Table 1 can be chosen as Type 1 or Table 2can be chosen as Type 2 Based on the range of 119889119894 the numberof bits to be hidden (119899119894) can be decided from the range table

Now convert each 119899119894 bits of confidential data to its decimalvalue 119889119904119894 for 119894 = 1 2 7 Then compute the new values forthe seven differences as 1198891015840

119894= 119897119894+119889119904119894 for 119894 = 1 2 7 Now for

each 119901119894 where 119894 = 1 2 7 calculate two new values 11990110158401015840119894=

1199011015840119888minus 1198891015840119894and 119901101584010158401015840

119894= 1199011015840119888+ 1198891015840119894 Select one of these two values as 1199011015840

119894

by applying (2) This 1199011015840119894is the stego value of 119901119894

The LSB + EMD Embedding Approach The first LSB of pixel1199018 is substituted by 0 and the next two LSBs are substitutedby two data bits After embedding say it is 1199011015840

8 The decimal

4 Mathematical Problems in Engineering

Table 3 Results of existing techniques

Images512 times 512 times 3

Wu and Tsai [5] Shen and Huang [23]PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4367 1232606 0999 156 3801 1223062 0998 155Baboon 3840 1403491 0998 178 4014 1343274 0999 170Peppers 4313 1174751 0999 149 4157 1226139 0999 155Jet 4397 1220544 0999 155 4335 1212350 0999 154Boat 4133 1278971 0999 162 4135 1264742 0999 160House 4127 1256404 0999 159 4175 1242081 0999 157Pot 4401 1163700 0999 147 4338 1195641 0999 152Average 4225 1247209 0999 157 4136 1243898 0999 158

P4 P3 P2

P5 Pc P1

P6 P7 P8

(a)

pc

p4

p1

p2p

3

p5

p6 p

7 p8

(b)

plowastc plowast

1

plowast2plowast

3plowast4

plowast5

plowast6 plowast

7 plowast8

(c)

Figure 2 (a) Cover pixel block (b) stego block and (c) stego block used for extraction

value of the three LSBs of 11990110158408is 1199042 and the decimal value of

three LSBs of1199018 is 1198942 Now calculate the difference df 2 as df2 =1198942 minus 1199042 Now optimize the value of 1199011015840

8using (4)

Suppose we denote the remaining pixels (1199011 1199012 1199013 11990141199015 1199016 1199017 119901119888) by a name 119901119896 where 119896 = 1 2 3 4 5 6 7 119888 Nowapply EMD for each 119901119896 as follows Each 119901119896 has to hide 2 bitsof data The decimal equivalent of the two data bits is 119898119896Now select 119909 from minus3 minus2 minus1 0 and calculate 11990110158401015840

119896= 119901119896 + 119909

such that the condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly

select 119909 from 1 2 3 and calculate 119901101584010158401015840119896= 119901119896 + 119909 such that

the condition (119901101584010158401015840119896

mod 4 = 119898119896) satisfies If for all the threevalues in list 1 2 3 the condition (119901101584010158401015840

119896mod 4 = 119898119896) does

not satisfy then set 119901101584010158401015840119896= minus10 Now calculate 1199011015840

119896by (3) This

1199011015840119896is the stego value of 119901119896Thus Figure 2(b) represents the stego-pixel block

32 The Extraction Procedure

Step 1 The stego image is traversed in raster scan orderand partitioned into nonoverlapping blocks of size 3 times 3Figure 2(c) represents a sample 3 times 3 stego-pixel block

Step 2 The LSB bit of 119901lowast8is checked if it is 1 then for this

block the extraction procedure of LSB + PVD approach isused as follows The three LSBs of 119901lowast

119888and next two LSBs

of 119901lowast8are extracted Furthermore the 119889lowast

119894= |119901lowast119888minus 119901lowast119894| and

119904lowast119894= 119889lowast119894minus 119897119894 for 119894 = 1 2 3 7 are calculated where 119889lowast

119894

belongs to the range 119877119894 and 119897119894 is the lower bound of this rangeNow each of these 119904lowast

119894is converted to 119899119894 binary bits where 119899119894

is the value corresponding to the same range 119877119894 of 119889lowast119894 Notethat the same range table (Table 1 or Table 2) which was usedduring embedding should be used during extraction

Step 3 If the LSB bit of 119901lowast8is 0 then for this block the

extraction procedure of LSB + EMD is applied as follows

The next two LSBs of 119901lowast8are extracted For all the remaining

pixels (119901lowast1 119901lowast2 119901lowast3 119901lowast4 119901lowast5 119901lowast6 119901lowast7 119901lowast119888) the decimal equivalent

of the embedded bits119898119896 is calculated as119898119896 = 119901lowast119896 mod 4 for119896 = 1 2 3 4 5 6 7 119888 Now each 119898119896 is converted to 2 binarybits

4 Results and DiscussionThe implementation work is done using MATLAB tool andwith the RGB color images The data hiding is performed inRed Green and Blue planes separately It can also be appliedon gray scale images Experiments are done with manyimages Few samples are shown here Figure 3 represents fouroriginal samples Figures 4 and 5 are their stego samples forType 1 and Type 2 of technique 1 respectively Figures 6 and7 are the stego samples for Type 1 and Type 2 of technique2 respectively Each stego image has hidden 700000 (sevenlakhs) bits of secret data These stego images look innocuousand no distortion is observable

In Table 3 the results of Wu and Tsairsquos PVD techniqueand Shen and Huangrsquos [23] PVD + EMD technique are givenIn Tables 4 and 5 the results of the proposed technique1 and technique 2 respectively are given These results arecomprised of four parameters (i) hiding capacity [1] (ii) bitsper byte (BPB) [8] (iii) PSNR [1] and (iv) quality index 119876[6]

It can be found from Tables 3 4 and 5 that the hidingcapacity and BPB of proposed technique 1 (Type 1 and Type2) and technique 2 (Type 1 and Type 2) are significantlyenhanced as compared to that of Wu and Tsai and Shen andHuangrsquos techniques Furthermore the PSNR of the proposedtechnique 1 (Type 1 and Type 2) and technique 2 (Type 1 andType 2) are nearly equal to that of Wu and Tsai and Shen andHuangrsquos techniques

Mathematical Problems in Engineering 5

Table 4 Results of proposed technique 1

Images512 times 512 times 3

Proposed 3 PVD + 3 LSB + EMD (Type 1) Proposed 3 PVD + 3 LSB + EMD (Type 2)PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4445 1631063 0999 207 4133 1687353 0999 215Baboon 3485 1898778 0997 241 3254 2237194 0994 284Peppers 4026 1635779 0999 208 3873 1693901 0999 215Jet 4288 1637898 0999 208 4204 1702029 0999 216Boat 3850 1708242 0999 217 3609 1840256 0998 234House 4023 1691500 0999 215 3918 1808544 0998 230Pot 4635 1599030 0999 203 4280 1622565 0999 206Average 4107 1686041 0999 214 3895 1798834 0998 228

Table 5 Results of proposed technique 2

Images512 times 512 times 3

Proposed 7 PVD + 3 LSB + EMD (Type 1) Proposed 7 PVD + 3 LSB + EMD (Type 2)PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4498 1639022 0999 209 4126 1690031 0999 215Baboon 3467 1987328 0996 254 3249 2338643 0994 298Peppers 3814 1640887 0998 209 3470 1693278 0997 216Jet 4300 1647786 0999 210 4046 1709098 0998 218Boat 3776 1740611 0998 222 3436 1873870 0997 239House 4012 1724458 0998 220 3879 1841047 0998 235Pot 4328 1596123 0999 204 3880 1617011 0999 206Average 4028 1710888 0998 218 3726 1823282 0998 232

(a) Lena (b) Baboon (c) Boat (d) Pot

Figure 3 Original images

Figure 4 Stego images of technique 1 (Type 1)

6 Mathematical Problems in Engineering

Figure 5 Stego images of technique 1 (Type 2)

Figure 6 Stego images of technique 2 (Type 1)

Figure 7 Stego images of technique 2 (Type 2)

Table 6 Average results of proposed techniques

Type BPB PSNRProposed 3 PVD + 3 LSB + EMD (Type 1) 214 4107Proposed 7 PVD + 3 LSB + EMD (Type 1) 218 4028Proposed 3 PVD + 3 LSB + EMD (Type 2) 228 3895Proposed 7 PVD + 3 LSB + EMD (Type 2) 232 3726

Furthermore the average performance of the proposedtechniques is compared with that of Kieu and Changrsquos [19]technique The average BPB and PSNR for the proposed twotechniques is as given in Table 6 Similarly the BPB and PSNRof Kieu and Changrsquos technique for different values of theparameter 119904 is as given in Table 7 By observing Table 6 wecan find that in the proposed techniqueswith BPB values 214218 228 and 232 the PSNR values are 4107 4028 3895and 3726 respectively By observing Table 7 we can find that

in the Kieu and Changrsquos technique with BPB values 1 2 3 and4 the PSNR values are 5239 4674 4082 and 3482 respec-tively Thus the PSNR and BPB values of Kieu and Changrsquostechnique (for 119904 = 6 BPB= 25 andPSNR=4329) are slightlybetter than that of the proposed techniques (BPB = 232 andPSNR = 4107) But there is no experimental evidence thatKieu and Changrsquos technique is undetectable by PDH analysisand RS analysis The proposed techniques are undetectableby PDH analysis it is experimentally proved in Figures 9 and10 It is also proved in Figures 11 and 12 that the proposedtechniques are undetectable by RS analysis PSNR and BPBare not only the measuring parameters security analysis isalso another parameter to be taken into consideration whilejudging the merit of a steganography technique

Now let us come to security analysis The PDH analysisdiagrams clearly reveal the step effects in Shen and Huangrsquostechnique Figures 8(a) and 8(b) Wu and Tsairsquos techniqueis also detected by PDH analysis proved in [25] But for

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

the proposed techniques Figures 9(a)ndash9(d) and Figures10(a)ndash10(d) the step effects are not observable

We can observe the RS analysis curves of the proposedtechnique 1 in Figure 11 In Lena image there is biggernumber of smooth blocks but in Baboon image there isbigger number of edge blocks For Baboon image curves for119877119898 and 119877minus119898 are linear and nearly parallel to each other

Similarly curves for 119878119898 and 119878minus119898 are linear and nearly parallelto each other Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898 isstrongly satisfied For Lena image curve for 119877119898 is linear andthe curve for 119877minus119898 is slightly diverging from it Similarlycurves for 119878119898 are linear and the curve for 119878minus119898 is slightlydiverging from it Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898is weakly satisfied for Lena image Figure 12 represents the RSanalysis for technique 2 In all the four cases the graphs for119877119898 and 119877minus119898 are linear and nearly overlap with one anotherand the graphs for 119878119898 and 119878minus119898 are linear and nearly overlapwith one another Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898is strongly satisfied Hence it can be concluded thatRS analysis cannot detect the proposed steganographytechniques

5 Conclusion

Shen and Huang proposed PVD in connection with EMD toachieve greater hiding capacity and higher PSNR But it isfound to be detectable by pixel difference histogram analysis

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

To fix this problem a combination of LSB substitution PVDand EMD is proposed in this paper The proposed technique1 and technique 2 operate on 2 times 2 and 3 times 3 pixel blocksrespectively by calculating the average of the pixel valuedifferences Based on this average value either PVD or EMD

is applied in combination with LSB Both the techniques givehigher hiding capacity compared to that of Shen and Huangrsquostechnique The recorded PSNR values are also as good asthat of Shen and Huangrsquos technique If we compare betweenthe two proposed techniques then Type 1 of technique 1 is

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

good for PSNR and Type 2 of technique 2 is good for hidingcapacity It has also been proved that the proposed techniquesare not detectable by RS analysis

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] A Cheddad J Condell K Curran and P Mc Kevitt ldquoDigitalimage steganography survey and analysis of current methodsrdquoSignal Processing vol 90 no 3 pp 727ndash752 2010

[2] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Mathematical Problems in Engineering 11

[3] G Swain and S K Lenka ldquoA technique for secret communi-cation using a new block cipher with dynamic steganographyrdquoInternational Journal of Security and its Applications vol 6 no2 pp 1ndash12 2012

[4] G Swain and S K Lenka ldquoA novel steganography technique bymapping words with LSB arrayrdquo International Journal of Signaland Imaging Systems Engineering vol 8 no 1-2 pp 115ndash1222015

[5] D-CWu andW-H Tsai ldquoA steganographicmethod for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[6] MKhodaei andK Faez ldquoNew adaptive steganographicmethodusing least-significant-bit substitution and pixel-value differ-encingrdquo IET Image Processing vol 6 no 6 pp 677ndash686 2012

[7] W Luo F Huang and J Huang ldquoA more secure steganographybased on adaptive pixel-value differencing schemerdquoMultimediaTools and Applications vol 52 no 2-3 pp 407ndash430 2011

[8] A Pradhan K R Sekhar and G Swain ldquoAdaptive PVDSteganography Using Horizontal Vertical and Diagonal Edgesin Six-Pixel Blocksrdquo Security andCommunication Networks vol2017 pp 1ndash13 2017

[9] X Liao Q Wen and J Zhang ldquoA steganographic methodfor digital images with four-pixel differencing and modifiedLSB substitutionrdquo Journal of Visual Communication and ImageRepresentation vol 22 no 1 pp 1ndash8 2011

[10] X Zhang and S Wang ldquoEfficient steganographic embeddingby exploiting modification directionrdquo IEEE CommunicationsLetters vol 10 no 11 pp 781ndash783 2006

[11] C-C Chang W-L Tai and K-N Chen ldquoImprovements ofEMD embedding for large payloadsrdquo in Proceedings of the 3rdInternational Conference on Intelligent Information Hiding andMultimedia Signal Processing IIHMSP 2007 vol 1 pp 473ndash476November 2007

[12] C-F Lee Y-R Wang and C-C Chang ldquoA steganographicmethod with high embedding capacity by improving exploitingmodification directionrdquo in Proceedings of the 3rd InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 497ndash500 November 2007

[13] C-F Lee C-C Chang and K-H Wang ldquoAn improvement ofEMD embedding method for large payloads by pixel segmenta-tion strategyrdquo Image and Vision Computing vol 26 no 12 pp1670ndash1676 2008

[14] K H Jung and K Y Yoo ldquoImproved modification directiontechnique by modulus operationrdquo International Journal ofSignal Processing Image Processing and Pattern vol 2 no 1 pp79ndash87 2009

[15] R Chao H Wu C Lee and Y Chu ldquoA Novel Image DataHiding Schemewith Diamond Encodingrdquo EURASIP Journal onInformation Security vol 2009 no 1 p 658047 2009

[16] J-C Joo H-Y Lee and H-K Lee ldquoImproved steganographicmethod preserving pixel-value differencing histogram withmodulus functionrdquo Eurasip Journal on Advances in SignalProcessing vol 2010 Article ID 249826 2010

[17] H J Kim C Kim S Wang and X Zhang ldquoImproved mod-ification direction methodsrdquo Computers amp Mathematics withApplications vol 60 no 2 pp 319ndash325 2010

[18] J Wang Y Sun H Xu K Chen H Joong Kim and S-H JooldquoAn improved section-wise exploiting modification directionmethodrdquo Signal Processing vol 90 no 11 pp 2954ndash2964 2010

[19] T D Kieu and C-C Chang ldquoA steganographic scheme byfully exploiting modification directionsrdquo Expert Systems withApplications vol 38 no 8 pp 10648ndash10657 2011

[20] X-T Wang C-C Chang C-C Lin and M-C Li ldquoA novelmulti-group exploiting modification direction method basedon switch maprdquo Signal Processing vol 92 no 6 pp 1525ndash15352012

[21] D-S Fu Z-J Jing S-G Zhao and J Fan ldquoReversible datahiding based on prediction-error histogram shifting and EMDmechanismrdquo AEU - International Journal of Electronics andCommunications vol 68 no 10 pp 933ndash943 2014

[22] C Kim ldquoData hiding by an improved exploiting modificationdirectionrdquoMultimedia Tools and Applications vol 69 no 3 pp569ndash584 2014

[23] S-Y Shen and L-H Huang ldquoA data hiding scheme usingpixel value differencing and improving exploiting modificationdirectionsrdquo Computers and Security vol 48 pp 131ndash141 2015

[24] A Soria-Lorente and S Berres ldquoA Secure SteganographicAlgorithmBased on FrequencyDomain for the Transmission ofHidden Informationrdquo Security and Communication Networksvol 2017 pp 1ndash14 2017

[25] A Pradhan K Raja Sekhar and G Swain ldquoDigital imagesteganography based on seven way pixel value differencingrdquoIndian Journal of Science and Technology vol 9 no 37 ArticleID 88557 2016

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Submit your manuscripts atwwwhindawicom

2 Mathematical Problems in Engineering

Pc P1

P2 P3

(a)

pc p

1

p2 p

3

(b)

plowastc plowast

1

plowast2 plowast

3

(c)

Figure 1 (a) Cover pixel block (b) stego block and (c) stego block used for extraction

increase the hiding capacity The EMD technique based ondiamond encoding also could improve the hiding capacity[15] Joo et alrsquos EMD technique using modulus functionpreserved the pixel difference histogram [16] Kim et al [17]has proposed two EMD techniques namely EMD-2 and 2-EMD In EMD-2 technique at most two pixels are modifiedand in 2-EMD technique two consecutive EMDs are usedBoth these techniques achieve higher hiding capacity Wanget al [18] said that a number of pixel groups could becombined to derive more number of embedding directionsso that distortion can be reduced Kieu and Changrsquos [19]EMD technique used eight modification directions It fullyexploited allmodification directions andmeasured the hidingcapacity and distortion for different values of the parameter 119904Wang et alrsquos [20] EMD technique combined multiple groupsto hide the data according to a designed switch map sothat the hiding capacity can be increased and distortioncan be decreased Fu et al [21] used EMD and multilayerembedding mechanism with histogram shifting to achievereversibility Kim [22] advanced the EMD technique usingbasis vector and (2119899+119909 minus 1)-ary notational system where119899 and 119909 are user defined values Shen and Huang [23]made the hiding capacity of a block adaptive by using PVDwith EMD This PVD with EMD technique provides higherhiding capacity and better PSNR To improve upon thesecurity keys are used to generate pseudo random num-bers which can be used to find the embedding locations[24]

It is found that Shen and Huangrsquos [23] PVD with EMDtechnique is detectable by PDH analysis To advance furtherin this paper we judiciously combined LSB substitution PVDand EMD techniques to protect against PDH analysis and topossess larger hiding capacity without sacrificing the PSNRThere are two techniques proposed the first technique isdesigned using 2 times 2 pixel blocks and the second techniqueis designed using 3 times 3 pixel blocks

2 The Proposed Technique 1 (LSB + PVD +EMD in 2 times 2 Pixel Blocks)

21 The Embedding Procedure

Step 1 The image is traversed in raster scan order andpartitioned into nonoverlapping blocks of size 2times 2 A sampleblock is shown in Figure 1(a)

Step 2 For every block the average pixel value difference 119889 =(13)sum3

119894=1|119875119888 minus 119875119894| is computed If 119889 is greater than 15 then

Table 1 Range table (Type 1)

Range119897119894 1199061198941198771 =0 71198772=

8 151198773=

16 311198774=

32 631198775=

64 1271198776=

128 255No of bitsto behidden 119899

119894

3 3 3 3 4 4

Table 2 Range table (Type 2)

Range119897119894 1199061198941198771 =0 71198772=

8 151198773=

16 311198774=

32 631198775=

64 1271198776=

128 255No of bitsto behidden 119899

119894

3 3 4 5 6 6

the block is said to be an edge area otherwise it is a smootharea

Step 3 In an edge area embedding is done using LSBsubstitution and PVD

Step 4 In a smooth area embedding is done using LSBsubstitution and EMD

TheLSB + PVDEmbedding Approach The first LSB of pixel119875119888is substituted by bit 1 to act as an indicator during extractionThe other 2 LSBs are substituted by 2 data bits A new valueof this pixel 1199011015840

119888is obtained Suppose the decimal value of the

three LSBs of 1199011015840119888is 1199041 and the decimal value of the three LSBs

of 119875119888 is 1198941 A difference value df1 = 1198941 minus 1199041 is calculated and 1199011015840119888

is optimized by

1199011015840119888=

1199011015840119888+ 23 if df1 gt 23minus1 0 le (1199011015840119888 + 23) le 2551199011015840119888minus 23 if df1 lt minus23minus1 0 le (1199011015840119888 minus 23) le 2551199011015840119888 otherwise

(1)

Now calculate three difference values 119889119894 = |1199011015840119888 minus 119901119894| for 119894 =1 2 3 It falls into one of the ranges in range table Based onthe range of 119889119894 the number of bits to be hidden (119899119894) can bedecided Table 1 can be referred to as Type 1 and Table 2 can bereferred to as Type 2 Now convert each 119899119894 bits of confidentialdata to its decimal value 119889119904119894 for 119894 = 1 2 3 Then compute thenew value for this difference as 1198891015840

119894= 119897119894 + 119889119904119894 for 119894 = 1 2 3

Now for each 119901119894 where 119894 = 1 2 3 calculate two new values

Mathematical Problems in Engineering 3

11990110158401015840119894= 1199011015840119888minus1198891015840119894and 119901101584010158401015840

119894= 1199011015840119888+1198891015840119894 Select one of these two values

as 1199011015840119894by applying

1199011015840119894=

11990110158401015840119894 if 10038161003816100381610038161003816119901119894 minus 119901

10158401015840

119894

10038161003816100381610038161003816 lt10038161003816100381610038161003816119901119894 minus 119901

101584010158401015840

119894

10038161003816100381610038161003816 0 le 11990110158401015840

119894le 255

119901101584010158401015840119894 otherwise

(2)

The LSB + EMD Embedding Approach The first LSB bit ofpixel 119901119888 is substituted by bit 0 which can act as an indicatorduring extraction The other two LSBs of 119901119888 are substituted bytwo data bits Thus a new value 1199011015840

119888of the pixel 119901119888 is obtained

Suppose the decimal value of the three LSBs of 1199011015840119888is 1199041 and

the decimal value of the three LSBs of 119875119888 is 1198941 A difference

value df1 = 1198941 minus 1199041 is calculated and 1199011015840119888is optimized by

(1)Suppose we denote the remaining pixels (1199011 1199012 1199013) by

a name 119901119896 where 119896 = 1 2 3 Now apply EMD for each 119901119896as follows Each 119901119896 has to hide 2 bits of data The decimalequivalent of the two data bits is 119898119896 Now select 119909 fromminus3 minus2 minus1 0 and calculate 11990110158401015840

119896= 119901119896 + 119909 such that the

condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly select 119909 from

1 2 3 and calculate 119901101584010158401015840119896= 119901119896 + 119909 such that the condition

(119901101584010158401015840119896

mod 4 = 119898119896) satisfies If for all the three values in list1 2 3 the condition (119901101584010158401015840

119896mod 4 = 119898119896) does not satisfy

then set 119901101584010158401015840119896= minus10 Now calculate the stego value 1199011015840

119896for 119901119896

by (3)

1199011015840119896=

11990110158401015840119896 if (119901101584010158401015840

119896lt 0 or 119901101584010158401015840

119896gt 255) 0 le 11990110158401015840

119896le 255 or 0 le (11990110158401015840

119896 119901101584010158401015840119896) le 255 10038161003816100381610038161003816119901119896 minus 119901

10158401015840

119896

10038161003816100381610038161003816 le10038161003816100381610038161003816119901119896 minus 119901

101584010158401015840

119896

10038161003816100381610038161003816119901101584010158401015840119896 if (11990110158401015840

119896lt 0 or 11990110158401015840

119896gt 255) 0 le 119901101584010158401015840

119896le 255 or 0 le (11990110158401015840

101584010158401015840

119896

10038161003816100381610038161003816 le10038161003816100381610038161003816119901119896 minus 119901

10158401015840

119896

10038161003816100381610038161003816(3)

Thus Figure 1(b) represents the stego-pixel block

22 The Extraction Procedure

Step 1 The stego image is traversed in raster scan orderand partitioned into nonoverlapping blocks of size 2 times 2Figure 1(c) represents a sample 2 times 2 stego-pixel block

Step 2 The LSB bit of 119901lowast119888is checked if it is 1 then for

this block the extraction procedure of LSB + PVD approachis used as follows The next two LSBs of 119901lowast

119888are extracted

Furthermore the 119889lowast119894= |119901lowast119888minus119901lowast119894| and 119904lowast

119894= 119889lowast119894minus119897119894 for 119894 = 1 2 3

are calculated where 119889lowast119894belongs to the range 119877119894 and 119897119894 is the

lower bound of this range Now each of these 119904lowast119894is converted

to 119899119894 binary bits where 119899119894 is the value corresponding to thesame range 119877119894 of 119889lowast119894 Note that the same range table (Table 1or Table 2) which was used during embedding should be usedduring extraction

Step 3 If the LSB bit of 119901lowast119888is 0 then for this block the

extraction procedure of LSB + EMD is applied as followsThenext two LSBs of119901lowast

119888are extracted For all the remaining pixels

(119901lowast1 119901lowast2 119901lowast3) the decimal equivalent of the embedded bits119898119896

is calculated as119898119896 = 119901lowast119896 mod 4 for 119896 = 1 2 3 Now each 119898119896is converted to 2 binary bits

3 The Proposed Technique 2 (LSB + PVD +EMD in 3 times 3 Pixel Blocks)

31 The Embedding Procedure

Step 1 The image is traversed in raster scan order andpartitioned into nonoverlapping blocks of size 3times 3 A sampleblock is shown in Figure 2(a)

Step 2 An average pixel value difference 119889 = (18)sum8119894=1|119875119888 minus

119875119894| is calculated

Step 3 If 119889 value is greater than 15 then a combination of LSBsubstitution and PVD is applied

Step 4 If 119889 value is less than or equal to 15 then a combina-tion of LSB substitution and EMD is applied

The LSB + PVD Embedding Approach In the central pixel119875119888 3 LSBs are substituted by 3 data bits A new value of thecentral pixel is found Say it is 1199011015840

119888 In pixel 1199018 the first LSB

is substituted by bit 1 which will be used as indicator duringextraction procedureThe other two LSBs in it are substitutedby two data bits After substituting three LSBs suppose thenew value of pixel 1199018 is 11990110158408 The decimal value of the threeLSBs of 1199011015840

119888is 1199041 and the decimal value of three LSBs of 119875119888 is

1198941 Similarly the decimal value of three LSBs of 11990110158408is 1199042 and

the decimal value of three LSBs of 1199018 is 1198942 Now calculate thedifferences df1 and df2 as df1 = 1198941 minus 1199041 and df2 = 1198942 minus 1199042 Nowoptimize the values of1199011015840

119888and11990110158408using (1) and (4) respectively

11990110158408=

11990110158408+ 23 if df2 gt 23minus1 0 le (11990110158408 + 23) le 25511990110158408minus 23 if df2 lt minus23minus1 0 le (11990110158408 minus 23) le 25511990110158408 otherwise

(4)

Now calculate seven difference values 119889119894 = |1199011015840119888 minus 119901119894| for119894 = 1 2 7 These difference values lie in one of the rangesof the range table Table 1 can be chosen as Type 1 or Table 2can be chosen as Type 2 Based on the range of 119889119894 the numberof bits to be hidden (119899119894) can be decided from the range table

Now convert each 119899119894 bits of confidential data to its decimalvalue 119889119904119894 for 119894 = 1 2 7 Then compute the new values forthe seven differences as 1198891015840

119894= 119897119894+119889119904119894 for 119894 = 1 2 7 Now for

each 119901119894 where 119894 = 1 2 7 calculate two new values 11990110158401015840119894=

1199011015840119888minus 1198891015840119894and 119901101584010158401015840

119894= 1199011015840119888+ 1198891015840119894 Select one of these two values as 1199011015840

119894

by applying (2) This 1199011015840119894is the stego value of 119901119894

The LSB + EMD Embedding Approach The first LSB of pixel1199018 is substituted by 0 and the next two LSBs are substitutedby two data bits After embedding say it is 1199011015840

8 The decimal

4 Mathematical Problems in Engineering

Table 3 Results of existing techniques

Images512 times 512 times 3

Wu and Tsai [5] Shen and Huang [23]PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4367 1232606 0999 156 3801 1223062 0998 155Baboon 3840 1403491 0998 178 4014 1343274 0999 170Peppers 4313 1174751 0999 149 4157 1226139 0999 155Jet 4397 1220544 0999 155 4335 1212350 0999 154Boat 4133 1278971 0999 162 4135 1264742 0999 160House 4127 1256404 0999 159 4175 1242081 0999 157Pot 4401 1163700 0999 147 4338 1195641 0999 152Average 4225 1247209 0999 157 4136 1243898 0999 158

P4 P3 P2

P5 Pc P1

P6 P7 P8

(a)

pc

p4

p1

p2p

3

p5

p6 p

7 p8

(b)

plowastc plowast

1

plowast2plowast

3plowast4

plowast5

plowast6 plowast

7 plowast8

(c)

Figure 2 (a) Cover pixel block (b) stego block and (c) stego block used for extraction

value of the three LSBs of 11990110158408is 1199042 and the decimal value of

three LSBs of1199018 is 1198942 Now calculate the difference df 2 as df2 =1198942 minus 1199042 Now optimize the value of 1199011015840

8using (4)

Suppose we denote the remaining pixels (1199011 1199012 1199013 11990141199015 1199016 1199017 119901119888) by a name 119901119896 where 119896 = 1 2 3 4 5 6 7 119888 Nowapply EMD for each 119901119896 as follows Each 119901119896 has to hide 2 bitsof data The decimal equivalent of the two data bits is 119898119896Now select 119909 from minus3 minus2 minus1 0 and calculate 11990110158401015840

119896= 119901119896 + 119909

such that the condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly

select 119909 from 1 2 3 and calculate 119901101584010158401015840119896= 119901119896 + 119909 such that

the condition (119901101584010158401015840119896

mod 4 = 119898119896) satisfies If for all the threevalues in list 1 2 3 the condition (119901101584010158401015840

119896mod 4 = 119898119896) does

not satisfy then set 119901101584010158401015840119896= minus10 Now calculate 1199011015840

119896by (3) This

1199011015840119896is the stego value of 119901119896Thus Figure 2(b) represents the stego-pixel block

32 The Extraction Procedure

Step 1 The stego image is traversed in raster scan orderand partitioned into nonoverlapping blocks of size 3 times 3Figure 2(c) represents a sample 3 times 3 stego-pixel block

Step 2 The LSB bit of 119901lowast8is checked if it is 1 then for this

block the extraction procedure of LSB + PVD approach isused as follows The three LSBs of 119901lowast

119888and next two LSBs

of 119901lowast8are extracted Furthermore the 119889lowast

119894= |119901lowast119888minus 119901lowast119894| and

119904lowast119894= 119889lowast119894minus 119897119894 for 119894 = 1 2 3 7 are calculated where 119889lowast

119894

belongs to the range 119877119894 and 119897119894 is the lower bound of this rangeNow each of these 119904lowast

119894is converted to 119899119894 binary bits where 119899119894

is the value corresponding to the same range 119877119894 of 119889lowast119894 Notethat the same range table (Table 1 or Table 2) which was usedduring embedding should be used during extraction

Step 3 If the LSB bit of 119901lowast8is 0 then for this block the

extraction procedure of LSB + EMD is applied as follows

The next two LSBs of 119901lowast8are extracted For all the remaining

pixels (119901lowast1 119901lowast2 119901lowast3 119901lowast4 119901lowast5 119901lowast6 119901lowast7 119901lowast119888) the decimal equivalent

of the embedded bits119898119896 is calculated as119898119896 = 119901lowast119896 mod 4 for119896 = 1 2 3 4 5 6 7 119888 Now each 119898119896 is converted to 2 binarybits

4 Results and DiscussionThe implementation work is done using MATLAB tool andwith the RGB color images The data hiding is performed inRed Green and Blue planes separately It can also be appliedon gray scale images Experiments are done with manyimages Few samples are shown here Figure 3 represents fouroriginal samples Figures 4 and 5 are their stego samples forType 1 and Type 2 of technique 1 respectively Figures 6 and7 are the stego samples for Type 1 and Type 2 of technique2 respectively Each stego image has hidden 700000 (sevenlakhs) bits of secret data These stego images look innocuousand no distortion is observable

In Table 3 the results of Wu and Tsairsquos PVD techniqueand Shen and Huangrsquos [23] PVD + EMD technique are givenIn Tables 4 and 5 the results of the proposed technique1 and technique 2 respectively are given These results arecomprised of four parameters (i) hiding capacity [1] (ii) bitsper byte (BPB) [8] (iii) PSNR [1] and (iv) quality index 119876[6]

It can be found from Tables 3 4 and 5 that the hidingcapacity and BPB of proposed technique 1 (Type 1 and Type2) and technique 2 (Type 1 and Type 2) are significantlyenhanced as compared to that of Wu and Tsai and Shen andHuangrsquos techniques Furthermore the PSNR of the proposedtechnique 1 (Type 1 and Type 2) and technique 2 (Type 1 andType 2) are nearly equal to that of Wu and Tsai and Shen andHuangrsquos techniques

Mathematical Problems in Engineering 5

Table 4 Results of proposed technique 1

Images512 times 512 times 3

Proposed 3 PVD + 3 LSB + EMD (Type 1) Proposed 3 PVD + 3 LSB + EMD (Type 2)PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4445 1631063 0999 207 4133 1687353 0999 215Baboon 3485 1898778 0997 241 3254 2237194 0994 284Peppers 4026 1635779 0999 208 3873 1693901 0999 215Jet 4288 1637898 0999 208 4204 1702029 0999 216Boat 3850 1708242 0999 217 3609 1840256 0998 234House 4023 1691500 0999 215 3918 1808544 0998 230Pot 4635 1599030 0999 203 4280 1622565 0999 206Average 4107 1686041 0999 214 3895 1798834 0998 228

Table 5 Results of proposed technique 2

Images512 times 512 times 3

Proposed 7 PVD + 3 LSB + EMD (Type 1) Proposed 7 PVD + 3 LSB + EMD (Type 2)PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4498 1639022 0999 209 4126 1690031 0999 215Baboon 3467 1987328 0996 254 3249 2338643 0994 298Peppers 3814 1640887 0998 209 3470 1693278 0997 216Jet 4300 1647786 0999 210 4046 1709098 0998 218Boat 3776 1740611 0998 222 3436 1873870 0997 239House 4012 1724458 0998 220 3879 1841047 0998 235Pot 4328 1596123 0999 204 3880 1617011 0999 206Average 4028 1710888 0998 218 3726 1823282 0998 232

(a) Lena (b) Baboon (c) Boat (d) Pot

Figure 3 Original images

Figure 4 Stego images of technique 1 (Type 1)

6 Mathematical Problems in Engineering

Figure 5 Stego images of technique 1 (Type 2)

Figure 6 Stego images of technique 2 (Type 1)

Figure 7 Stego images of technique 2 (Type 2)

Table 6 Average results of proposed techniques

Type BPB PSNRProposed 3 PVD + 3 LSB + EMD (Type 1) 214 4107Proposed 7 PVD + 3 LSB + EMD (Type 1) 218 4028Proposed 3 PVD + 3 LSB + EMD (Type 2) 228 3895Proposed 7 PVD + 3 LSB + EMD (Type 2) 232 3726

Furthermore the average performance of the proposedtechniques is compared with that of Kieu and Changrsquos [19]technique The average BPB and PSNR for the proposed twotechniques is as given in Table 6 Similarly the BPB and PSNRof Kieu and Changrsquos technique for different values of theparameter 119904 is as given in Table 7 By observing Table 6 wecan find that in the proposed techniqueswith BPB values 214218 228 and 232 the PSNR values are 4107 4028 3895and 3726 respectively By observing Table 7 we can find that

in the Kieu and Changrsquos technique with BPB values 1 2 3 and4 the PSNR values are 5239 4674 4082 and 3482 respec-tively Thus the PSNR and BPB values of Kieu and Changrsquostechnique (for 119904 = 6 BPB= 25 andPSNR=4329) are slightlybetter than that of the proposed techniques (BPB = 232 andPSNR = 4107) But there is no experimental evidence thatKieu and Changrsquos technique is undetectable by PDH analysisand RS analysis The proposed techniques are undetectableby PDH analysis it is experimentally proved in Figures 9 and10 It is also proved in Figures 11 and 12 that the proposedtechniques are undetectable by RS analysis PSNR and BPBare not only the measuring parameters security analysis isalso another parameter to be taken into consideration whilejudging the merit of a steganography technique

Now let us come to security analysis The PDH analysisdiagrams clearly reveal the step effects in Shen and Huangrsquostechnique Figures 8(a) and 8(b) Wu and Tsairsquos techniqueis also detected by PDH analysis proved in [25] But for

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

the proposed techniques Figures 9(a)ndash9(d) and Figures10(a)ndash10(d) the step effects are not observable

We can observe the RS analysis curves of the proposedtechnique 1 in Figure 11 In Lena image there is biggernumber of smooth blocks but in Baboon image there isbigger number of edge blocks For Baboon image curves for119877119898 and 119877minus119898 are linear and nearly parallel to each other

Similarly curves for 119878119898 and 119878minus119898 are linear and nearly parallelto each other Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898 isstrongly satisfied For Lena image curve for 119877119898 is linear andthe curve for 119877minus119898 is slightly diverging from it Similarlycurves for 119878119898 are linear and the curve for 119878minus119898 is slightlydiverging from it Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898is weakly satisfied for Lena image Figure 12 represents the RSanalysis for technique 2 In all the four cases the graphs for119877119898 and 119877minus119898 are linear and nearly overlap with one anotherand the graphs for 119878119898 and 119878minus119898 are linear and nearly overlapwith one another Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898is strongly satisfied Hence it can be concluded thatRS analysis cannot detect the proposed steganographytechniques

5 Conclusion

Shen and Huang proposed PVD in connection with EMD toachieve greater hiding capacity and higher PSNR But it isfound to be detectable by pixel difference histogram analysis

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

To fix this problem a combination of LSB substitution PVDand EMD is proposed in this paper The proposed technique1 and technique 2 operate on 2 times 2 and 3 times 3 pixel blocksrespectively by calculating the average of the pixel valuedifferences Based on this average value either PVD or EMD

is applied in combination with LSB Both the techniques givehigher hiding capacity compared to that of Shen and Huangrsquostechnique The recorded PSNR values are also as good asthat of Shen and Huangrsquos technique If we compare betweenthe two proposed techniques then Type 1 of technique 1 is

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

good for PSNR and Type 2 of technique 2 is good for hidingcapacity It has also been proved that the proposed techniquesare not detectable by RS analysis

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] A Cheddad J Condell K Curran and P Mc Kevitt ldquoDigitalimage steganography survey and analysis of current methodsrdquoSignal Processing vol 90 no 3 pp 727ndash752 2010

[2] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Mathematical Problems in Engineering 11

[3] G Swain and S K Lenka ldquoA technique for secret communi-cation using a new block cipher with dynamic steganographyrdquoInternational Journal of Security and its Applications vol 6 no2 pp 1ndash12 2012

[4] G Swain and S K Lenka ldquoA novel steganography technique bymapping words with LSB arrayrdquo International Journal of Signaland Imaging Systems Engineering vol 8 no 1-2 pp 115ndash1222015

[5] D-CWu andW-H Tsai ldquoA steganographicmethod for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[6] MKhodaei andK Faez ldquoNew adaptive steganographicmethodusing least-significant-bit substitution and pixel-value differ-encingrdquo IET Image Processing vol 6 no 6 pp 677ndash686 2012

[7] W Luo F Huang and J Huang ldquoA more secure steganographybased on adaptive pixel-value differencing schemerdquoMultimediaTools and Applications vol 52 no 2-3 pp 407ndash430 2011

[8] A Pradhan K R Sekhar and G Swain ldquoAdaptive PVDSteganography Using Horizontal Vertical and Diagonal Edgesin Six-Pixel Blocksrdquo Security andCommunication Networks vol2017 pp 1ndash13 2017

[9] X Liao Q Wen and J Zhang ldquoA steganographic methodfor digital images with four-pixel differencing and modifiedLSB substitutionrdquo Journal of Visual Communication and ImageRepresentation vol 22 no 1 pp 1ndash8 2011

[10] X Zhang and S Wang ldquoEfficient steganographic embeddingby exploiting modification directionrdquo IEEE CommunicationsLetters vol 10 no 11 pp 781ndash783 2006

[11] C-C Chang W-L Tai and K-N Chen ldquoImprovements ofEMD embedding for large payloadsrdquo in Proceedings of the 3rdInternational Conference on Intelligent Information Hiding andMultimedia Signal Processing IIHMSP 2007 vol 1 pp 473ndash476November 2007

[12] C-F Lee Y-R Wang and C-C Chang ldquoA steganographicmethod with high embedding capacity by improving exploitingmodification directionrdquo in Proceedings of the 3rd InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 497ndash500 November 2007

[13] C-F Lee C-C Chang and K-H Wang ldquoAn improvement ofEMD embedding method for large payloads by pixel segmenta-tion strategyrdquo Image and Vision Computing vol 26 no 12 pp1670ndash1676 2008

[14] K H Jung and K Y Yoo ldquoImproved modification directiontechnique by modulus operationrdquo International Journal ofSignal Processing Image Processing and Pattern vol 2 no 1 pp79ndash87 2009

[15] R Chao H Wu C Lee and Y Chu ldquoA Novel Image DataHiding Schemewith Diamond Encodingrdquo EURASIP Journal onInformation Security vol 2009 no 1 p 658047 2009

[16] J-C Joo H-Y Lee and H-K Lee ldquoImproved steganographicmethod preserving pixel-value differencing histogram withmodulus functionrdquo Eurasip Journal on Advances in SignalProcessing vol 2010 Article ID 249826 2010

[17] H J Kim C Kim S Wang and X Zhang ldquoImproved mod-ification direction methodsrdquo Computers amp Mathematics withApplications vol 60 no 2 pp 319ndash325 2010

[18] J Wang Y Sun H Xu K Chen H Joong Kim and S-H JooldquoAn improved section-wise exploiting modification directionmethodrdquo Signal Processing vol 90 no 11 pp 2954ndash2964 2010

[19] T D Kieu and C-C Chang ldquoA steganographic scheme byfully exploiting modification directionsrdquo Expert Systems withApplications vol 38 no 8 pp 10648ndash10657 2011

[20] X-T Wang C-C Chang C-C Lin and M-C Li ldquoA novelmulti-group exploiting modification direction method basedon switch maprdquo Signal Processing vol 92 no 6 pp 1525ndash15352012

[21] D-S Fu Z-J Jing S-G Zhao and J Fan ldquoReversible datahiding based on prediction-error histogram shifting and EMDmechanismrdquo AEU - International Journal of Electronics andCommunications vol 68 no 10 pp 933ndash943 2014

[22] C Kim ldquoData hiding by an improved exploiting modificationdirectionrdquoMultimedia Tools and Applications vol 69 no 3 pp569ndash584 2014

[23] S-Y Shen and L-H Huang ldquoA data hiding scheme usingpixel value differencing and improving exploiting modificationdirectionsrdquo Computers and Security vol 48 pp 131ndash141 2015

[24] A Soria-Lorente and S Berres ldquoA Secure SteganographicAlgorithmBased on FrequencyDomain for the Transmission ofHidden Informationrdquo Security and Communication Networksvol 2017 pp 1ndash14 2017

[25] A Pradhan K Raja Sekhar and G Swain ldquoDigital imagesteganography based on seven way pixel value differencingrdquoIndian Journal of Science and Technology vol 9 no 37 ArticleID 88557 2016

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Mathematical Problems in Engineering 3

11990110158401015840119894= 1199011015840119888minus1198891015840119894and 119901101584010158401015840

119894= 1199011015840119888+1198891015840119894 Select one of these two values

as 1199011015840119894by applying

1199011015840119894=

11990110158401015840119894 if 10038161003816100381610038161003816119901119894 minus 119901

10158401015840

119894

10038161003816100381610038161003816 lt10038161003816100381610038161003816119901119894 minus 119901

101584010158401015840

119894

10038161003816100381610038161003816 0 le 11990110158401015840

119894le 255

119901101584010158401015840119894 otherwise

(2)

The LSB + EMD Embedding Approach The first LSB bit ofpixel 119901119888 is substituted by bit 0 which can act as an indicatorduring extraction The other two LSBs of 119901119888 are substituted bytwo data bits Thus a new value 1199011015840

119888of the pixel 119901119888 is obtained

Suppose the decimal value of the three LSBs of 1199011015840119888is 1199041 and

the decimal value of the three LSBs of 119875119888 is 1198941 A difference

value df1 = 1198941 minus 1199041 is calculated and 1199011015840119888is optimized by

(1)Suppose we denote the remaining pixels (1199011 1199012 1199013) by

a name 119901119896 where 119896 = 1 2 3 Now apply EMD for each 119901119896as follows Each 119901119896 has to hide 2 bits of data The decimalequivalent of the two data bits is 119898119896 Now select 119909 fromminus3 minus2 minus1 0 and calculate 11990110158401015840

119896= 119901119896 + 119909 such that the

condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly select 119909 from

1 2 3 and calculate 119901101584010158401015840119896= 119901119896 + 119909 such that the condition

(119901101584010158401015840119896

mod 4 = 119898119896) satisfies If for all the three values in list1 2 3 the condition (119901101584010158401015840

119896mod 4 = 119898119896) does not satisfy

then set 119901101584010158401015840119896= minus10 Now calculate the stego value 1199011015840

119896for 119901119896

by (3)

1199011015840119896=

11990110158401015840119896 if (119901101584010158401015840

119896lt 0 or 119901101584010158401015840

119896gt 255) 0 le 11990110158401015840

119896le 255 or 0 le (11990110158401015840

10158401015840

119896

10038161003816100381610038161003816 le10038161003816100381610038161003816119901119896 minus 119901

101584010158401015840

119896

10038161003816100381610038161003816119901101584010158401015840119896 if (11990110158401015840

119896lt 0 or 11990110158401015840

119896gt 255) 0 le 119901101584010158401015840

119896le 255 or 0 le (11990110158401015840

101584010158401015840

119896

10038161003816100381610038161003816 le10038161003816100381610038161003816119901119896 minus 119901

10158401015840

119896

10038161003816100381610038161003816(3)

Thus Figure 1(b) represents the stego-pixel block

22 The Extraction Procedure

Step 1 The stego image is traversed in raster scan orderand partitioned into nonoverlapping blocks of size 2 times 2Figure 1(c) represents a sample 2 times 2 stego-pixel block

Step 2 The LSB bit of 119901lowast119888is checked if it is 1 then for

this block the extraction procedure of LSB + PVD approachis used as follows The next two LSBs of 119901lowast

119888are extracted

Furthermore the 119889lowast119894= |119901lowast119888minus119901lowast119894| and 119904lowast

119894= 119889lowast119894minus119897119894 for 119894 = 1 2 3

are calculated where 119889lowast119894belongs to the range 119877119894 and 119897119894 is the

lower bound of this range Now each of these 119904lowast119894is converted

to 119899119894 binary bits where 119899119894 is the value corresponding to thesame range 119877119894 of 119889lowast119894 Note that the same range table (Table 1or Table 2) which was used during embedding should be usedduring extraction

Step 3 If the LSB bit of 119901lowast119888is 0 then for this block the

extraction procedure of LSB + EMD is applied as followsThenext two LSBs of119901lowast

119888are extracted For all the remaining pixels

(119901lowast1 119901lowast2 119901lowast3) the decimal equivalent of the embedded bits119898119896

is calculated as119898119896 = 119901lowast119896 mod 4 for 119896 = 1 2 3 Now each 119898119896is converted to 2 binary bits

3 The Proposed Technique 2 (LSB + PVD +EMD in 3 times 3 Pixel Blocks)

31 The Embedding Procedure

Step 1 The image is traversed in raster scan order andpartitioned into nonoverlapping blocks of size 3times 3 A sampleblock is shown in Figure 2(a)

Step 2 An average pixel value difference 119889 = (18)sum8119894=1|119875119888 minus

119875119894| is calculated

Step 3 If 119889 value is greater than 15 then a combination of LSBsubstitution and PVD is applied

Step 4 If 119889 value is less than or equal to 15 then a combina-tion of LSB substitution and EMD is applied

The LSB + PVD Embedding Approach In the central pixel119875119888 3 LSBs are substituted by 3 data bits A new value of thecentral pixel is found Say it is 1199011015840

119888 In pixel 1199018 the first LSB

is substituted by bit 1 which will be used as indicator duringextraction procedureThe other two LSBs in it are substitutedby two data bits After substituting three LSBs suppose thenew value of pixel 1199018 is 11990110158408 The decimal value of the threeLSBs of 1199011015840

119888is 1199041 and the decimal value of three LSBs of 119875119888 is

1198941 Similarly the decimal value of three LSBs of 11990110158408is 1199042 and

the decimal value of three LSBs of 1199018 is 1198942 Now calculate thedifferences df1 and df2 as df1 = 1198941 minus 1199041 and df2 = 1198942 minus 1199042 Nowoptimize the values of1199011015840

119888and11990110158408using (1) and (4) respectively

11990110158408=

11990110158408+ 23 if df2 gt 23minus1 0 le (11990110158408 + 23) le 25511990110158408minus 23 if df2 lt minus23minus1 0 le (11990110158408 minus 23) le 25511990110158408 otherwise

(4)

Now calculate seven difference values 119889119894 = |1199011015840119888 minus 119901119894| for119894 = 1 2 7 These difference values lie in one of the rangesof the range table Table 1 can be chosen as Type 1 or Table 2can be chosen as Type 2 Based on the range of 119889119894 the numberof bits to be hidden (119899119894) can be decided from the range table

Now convert each 119899119894 bits of confidential data to its decimalvalue 119889119904119894 for 119894 = 1 2 7 Then compute the new values forthe seven differences as 1198891015840

119894= 119897119894+119889119904119894 for 119894 = 1 2 7 Now for

each 119901119894 where 119894 = 1 2 7 calculate two new values 11990110158401015840119894=

1199011015840119888minus 1198891015840119894and 119901101584010158401015840

119894= 1199011015840119888+ 1198891015840119894 Select one of these two values as 1199011015840

119894

by applying (2) This 1199011015840119894is the stego value of 119901119894

The LSB + EMD Embedding Approach The first LSB of pixel1199018 is substituted by 0 and the next two LSBs are substitutedby two data bits After embedding say it is 1199011015840

8 The decimal

4 Mathematical Problems in Engineering

Table 3 Results of existing techniques

Images512 times 512 times 3

Wu and Tsai [5] Shen and Huang [23]PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4367 1232606 0999 156 3801 1223062 0998 155Baboon 3840 1403491 0998 178 4014 1343274 0999 170Peppers 4313 1174751 0999 149 4157 1226139 0999 155Jet 4397 1220544 0999 155 4335 1212350 0999 154Boat 4133 1278971 0999 162 4135 1264742 0999 160House 4127 1256404 0999 159 4175 1242081 0999 157Pot 4401 1163700 0999 147 4338 1195641 0999 152Average 4225 1247209 0999 157 4136 1243898 0999 158

P4 P3 P2

P5 Pc P1

P6 P7 P8

(a)

pc

p4

p1

p2p

3

p5

p6 p

7 p8

(b)

plowastc plowast

1

plowast2plowast

3plowast4

plowast5

plowast6 plowast

7 plowast8

(c)

Figure 2 (a) Cover pixel block (b) stego block and (c) stego block used for extraction

value of the three LSBs of 11990110158408is 1199042 and the decimal value of

three LSBs of1199018 is 1198942 Now calculate the difference df 2 as df2 =1198942 minus 1199042 Now optimize the value of 1199011015840

8using (4)

Suppose we denote the remaining pixels (1199011 1199012 1199013 11990141199015 1199016 1199017 119901119888) by a name 119901119896 where 119896 = 1 2 3 4 5 6 7 119888 Nowapply EMD for each 119901119896 as follows Each 119901119896 has to hide 2 bitsof data The decimal equivalent of the two data bits is 119898119896Now select 119909 from minus3 minus2 minus1 0 and calculate 11990110158401015840

119896= 119901119896 + 119909

such that the condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly

select 119909 from 1 2 3 and calculate 119901101584010158401015840119896= 119901119896 + 119909 such that

the condition (119901101584010158401015840119896

mod 4 = 119898119896) satisfies If for all the threevalues in list 1 2 3 the condition (119901101584010158401015840

119896mod 4 = 119898119896) does

not satisfy then set 119901101584010158401015840119896= minus10 Now calculate 1199011015840

119896by (3) This

1199011015840119896is the stego value of 119901119896Thus Figure 2(b) represents the stego-pixel block

32 The Extraction Procedure

Step 1 The stego image is traversed in raster scan orderand partitioned into nonoverlapping blocks of size 3 times 3Figure 2(c) represents a sample 3 times 3 stego-pixel block

Step 2 The LSB bit of 119901lowast8is checked if it is 1 then for this

block the extraction procedure of LSB + PVD approach isused as follows The three LSBs of 119901lowast

119888and next two LSBs

of 119901lowast8are extracted Furthermore the 119889lowast

119894= |119901lowast119888minus 119901lowast119894| and

119904lowast119894= 119889lowast119894minus 119897119894 for 119894 = 1 2 3 7 are calculated where 119889lowast

119894

belongs to the range 119877119894 and 119897119894 is the lower bound of this rangeNow each of these 119904lowast

119894is converted to 119899119894 binary bits where 119899119894

is the value corresponding to the same range 119877119894 of 119889lowast119894 Notethat the same range table (Table 1 or Table 2) which was usedduring embedding should be used during extraction

Step 3 If the LSB bit of 119901lowast8is 0 then for this block the

extraction procedure of LSB + EMD is applied as follows

The next two LSBs of 119901lowast8are extracted For all the remaining

pixels (119901lowast1 119901lowast2 119901lowast3 119901lowast4 119901lowast5 119901lowast6 119901lowast7 119901lowast119888) the decimal equivalent

of the embedded bits119898119896 is calculated as119898119896 = 119901lowast119896 mod 4 for119896 = 1 2 3 4 5 6 7 119888 Now each 119898119896 is converted to 2 binarybits

4 Results and DiscussionThe implementation work is done using MATLAB tool andwith the RGB color images The data hiding is performed inRed Green and Blue planes separately It can also be appliedon gray scale images Experiments are done with manyimages Few samples are shown here Figure 3 represents fouroriginal samples Figures 4 and 5 are their stego samples forType 1 and Type 2 of technique 1 respectively Figures 6 and7 are the stego samples for Type 1 and Type 2 of technique2 respectively Each stego image has hidden 700000 (sevenlakhs) bits of secret data These stego images look innocuousand no distortion is observable

In Table 3 the results of Wu and Tsairsquos PVD techniqueand Shen and Huangrsquos [23] PVD + EMD technique are givenIn Tables 4 and 5 the results of the proposed technique1 and technique 2 respectively are given These results arecomprised of four parameters (i) hiding capacity [1] (ii) bitsper byte (BPB) [8] (iii) PSNR [1] and (iv) quality index 119876[6]

It can be found from Tables 3 4 and 5 that the hidingcapacity and BPB of proposed technique 1 (Type 1 and Type2) and technique 2 (Type 1 and Type 2) are significantlyenhanced as compared to that of Wu and Tsai and Shen andHuangrsquos techniques Furthermore the PSNR of the proposedtechnique 1 (Type 1 and Type 2) and technique 2 (Type 1 andType 2) are nearly equal to that of Wu and Tsai and Shen andHuangrsquos techniques

Mathematical Problems in Engineering 5

Table 4 Results of proposed technique 1

Images512 times 512 times 3

Proposed 3 PVD + 3 LSB + EMD (Type 1) Proposed 3 PVD + 3 LSB + EMD (Type 2)PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4445 1631063 0999 207 4133 1687353 0999 215Baboon 3485 1898778 0997 241 3254 2237194 0994 284Peppers 4026 1635779 0999 208 3873 1693901 0999 215Jet 4288 1637898 0999 208 4204 1702029 0999 216Boat 3850 1708242 0999 217 3609 1840256 0998 234House 4023 1691500 0999 215 3918 1808544 0998 230Pot 4635 1599030 0999 203 4280 1622565 0999 206Average 4107 1686041 0999 214 3895 1798834 0998 228

Table 5 Results of proposed technique 2

Images512 times 512 times 3

Proposed 7 PVD + 3 LSB + EMD (Type 1) Proposed 7 PVD + 3 LSB + EMD (Type 2)PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

Lena 4498 1639022 0999 209 4126 1690031 0999 215Baboon 3467 1987328 0996 254 3249 2338643 0994 298Peppers 3814 1640887 0998 209 3470 1693278 0997 216Jet 4300 1647786 0999 210 4046 1709098 0998 218Boat 3776 1740611 0998 222 3436 1873870 0997 239House 4012 1724458 0998 220 3879 1841047 0998 235Pot 4328 1596123 0999 204 3880 1617011 0999 206Average 4028 1710888 0998 218 3726 1823282 0998 232

(a) Lena (b) Baboon (c) Boat (d) Pot

Figure 3 Original images

Figure 4 Stego images of technique 1 (Type 1)

6 Mathematical Problems in Engineering

Figure 5 Stego images of technique 1 (Type 2)

Figure 6 Stego images of technique 2 (Type 1)

Figure 7 Stego images of technique 2 (Type 2)

Table 6 Average results of proposed techniques

Type BPB PSNRProposed 3 PVD + 3 LSB + EMD (Type 1) 214 4107Proposed 7 PVD + 3 LSB + EMD (Type 1) 218 4028Proposed 3 PVD + 3 LSB + EMD (Type 2) 228 3895Proposed 7 PVD + 3 LSB + EMD (Type 2) 232 3726

Furthermore the average performance of the proposedtechniques is compared with that of Kieu and Changrsquos [19]technique The average BPB and PSNR for the proposed twotechniques is as given in Table 6 Similarly the BPB and PSNRof Kieu and Changrsquos technique for different values of theparameter 119904 is as given in Table 7 By observing Table 6 wecan find that in the proposed techniqueswith BPB values 214218 228 and 232 the PSNR values are 4107 4028 3895and 3726 respectively By observing Table 7 we can find that

in the Kieu and Changrsquos technique with BPB values 1 2 3 and4 the PSNR values are 5239 4674 4082 and 3482 respec-tively Thus the PSNR and BPB values of Kieu and Changrsquostechnique (for 119904 = 6 BPB= 25 andPSNR=4329) are slightlybetter than that of the proposed techniques (BPB = 232 andPSNR = 4107) But there is no experimental evidence thatKieu and Changrsquos technique is undetectable by PDH analysisand RS analysis The proposed techniques are undetectableby PDH analysis it is experimentally proved in Figures 9 and10 It is also proved in Figures 11 and 12 that the proposedtechniques are undetectable by RS analysis PSNR and BPBare not only the measuring parameters security analysis isalso another parameter to be taken into consideration whilejudging the merit of a steganography technique

Now let us come to security analysis The PDH analysisdiagrams clearly reveal the step effects in Shen and Huangrsquostechnique Figures 8(a) and 8(b) Wu and Tsairsquos techniqueis also detected by PDH analysis proved in [25] But for

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

the proposed techniques Figures 9(a)ndash9(d) and Figures10(a)ndash10(d) the step effects are not observable

We can observe the RS analysis curves of the proposedtechnique 1 in Figure 11 In Lena image there is biggernumber of smooth blocks but in Baboon image there isbigger number of edge blocks For Baboon image curves for119877119898 and 119877minus119898 are linear and nearly parallel to each other

Similarly curves for 119878119898 and 119878minus119898 are linear and nearly parallelto each other Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898 isstrongly satisfied For Lena image curve for 119877119898 is linear andthe curve for 119877minus119898 is slightly diverging from it Similarlycurves for 119878119898 are linear and the curve for 119878minus119898 is slightlydiverging from it Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898is weakly satisfied for Lena image Figure 12 represents the RSanalysis for technique 2 In all the four cases the graphs for119877119898 and 119877minus119898 are linear and nearly overlap with one anotherand the graphs for 119878119898 and 119878minus119898 are linear and nearly overlapwith one another Hence the relation 119877119898 cong 119877minus119898 gt 119878119898 cong 119878minus119898is strongly satisfied Hence it can be concluded thatRS analysis cannot detect the proposed steganographytechniques

5 Conclusion

Shen and Huang proposed PVD in connection with EMD toachieve greater hiding capacity and higher PSNR But it isfound to be detectable by pixel difference histogram analysis

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

To fix this problem a combination of LSB substitution PVDand EMD is proposed in this paper The proposed technique1 and technique 2 operate on 2 times 2 and 3 times 3 pixel blocksrespectively by calculating the average of the pixel valuedifferences Based on this average value either PVD or EMD

is applied in combination with LSB Both the techniques givehigher hiding capacity compared to that of Shen and Huangrsquostechnique The recorded PSNR values are also as good asthat of Shen and Huangrsquos technique If we compare betweenthe two proposed techniques then Type 1 of technique 1 is

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

good for PSNR and Type 2 of technique 2 is good for hidingcapacity It has also been proved that the proposed techniquesare not detectable by RS analysis

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] A Cheddad J Condell K Curran and P Mc Kevitt ldquoDigitalimage steganography survey and analysis of current methodsrdquoSignal Processing vol 90 no 3 pp 727ndash752 2010

[2] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Mathematical Problems in Engineering 11

[3] G Swain and S K Lenka ldquoA technique for secret communi-cation using a new block cipher with dynamic steganographyrdquoInternational Journal of Security and its Applications vol 6 no2 pp 1ndash12 2012

[4] G Swain and S K Lenka ldquoA novel steganography technique bymapping words with LSB arrayrdquo International Journal of Signaland Imaging Systems Engineering vol 8 no 1-2 pp 115ndash1222015

[5] D-CWu andW-H Tsai ldquoA steganographicmethod for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[6] MKhodaei andK Faez ldquoNew adaptive steganographicmethodusing least-significant-bit substitution and pixel-value differ-encingrdquo IET Image Processing vol 6 no 6 pp 677ndash686 2012

[7] W Luo F Huang and J Huang ldquoA more secure steganographybased on adaptive pixel-value differencing schemerdquoMultimediaTools and Applications vol 52 no 2-3 pp 407ndash430 2011

[8] A Pradhan K R Sekhar and G Swain ldquoAdaptive PVDSteganography Using Horizontal Vertical and Diagonal Edgesin Six-Pixel Blocksrdquo Security andCommunication Networks vol2017 pp 1ndash13 2017

[9] X Liao Q Wen and J Zhang ldquoA steganographic methodfor digital images with four-pixel differencing and modifiedLSB substitutionrdquo Journal of Visual Communication and ImageRepresentation vol 22 no 1 pp 1ndash8 2011

[10] X Zhang and S Wang ldquoEfficient steganographic embeddingby exploiting modification directionrdquo IEEE CommunicationsLetters vol 10 no 11 pp 781ndash783 2006

[11] C-C Chang W-L Tai and K-N Chen ldquoImprovements ofEMD embedding for large payloadsrdquo in Proceedings of the 3rdInternational Conference on Intelligent Information Hiding andMultimedia Signal Processing IIHMSP 2007 vol 1 pp 473ndash476November 2007

[12] C-F Lee Y-R Wang and C-C Chang ldquoA steganographicmethod with high embedding capacity by improving exploitingmodification directionrdquo in Proceedings of the 3rd InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 497ndash500 November 2007

[13] C-F Lee C-C Chang and K-H Wang ldquoAn improvement ofEMD embedding method for large payloads by pixel segmenta-tion strategyrdquo Image and Vision Computing vol 26 no 12 pp1670ndash1676 2008

[14] K H Jung and K Y Yoo ldquoImproved modification directiontechnique by modulus operationrdquo International Journal ofSignal Processing Image Processing and Pattern vol 2 no 1 pp79ndash87 2009

[15] R Chao H Wu C Lee and Y Chu ldquoA Novel Image DataHiding Schemewith Diamond Encodingrdquo EURASIP Journal onInformation Security vol 2009 no 1 p 658047 2009

[16] J-C Joo H-Y Lee and H-K Lee ldquoImproved steganographicmethod preserving pixel-value differencing histogram withmodulus functionrdquo Eurasip Journal on Advances in SignalProcessing vol 2010 Article ID 249826 2010

[17] H J Kim C Kim S Wang and X Zhang ldquoImproved mod-ification direction methodsrdquo Computers amp Mathematics withApplications vol 60 no 2 pp 319ndash325 2010

[18] J Wang Y Sun H Xu K Chen H Joong Kim and S-H JooldquoAn improved section-wise exploiting modification directionmethodrdquo Signal Processing vol 90 no 11 pp 2954ndash2964 2010

[19] T D Kieu and C-C Chang ldquoA steganographic scheme byfully exploiting modification directionsrdquo Expert Systems withApplications vol 38 no 8 pp 10648ndash10657 2011

[20] X-T Wang C-C Chang C-C Lin and M-C Li ldquoA novelmulti-group exploiting modification direction method basedon switch maprdquo Signal Processing vol 92 no 6 pp 1525ndash15352012

[21] D-S Fu Z-J Jing S-G Zhao and J Fan ldquoReversible datahiding based on prediction-error histogram shifting and EMDmechanismrdquo AEU - International Journal of Electronics andCommunications vol 68 no 10 pp 933ndash943 2014

[22] C Kim ldquoData hiding by an improved exploiting modificationdirectionrdquoMultimedia Tools and Applications vol 69 no 3 pp569ndash584 2014

[23] S-Y Shen and L-H Huang ldquoA data hiding scheme usingpixel value differencing and improving exploiting modificationdirectionsrdquo Computers and Security vol 48 pp 131ndash141 2015

[24] A Soria-Lorente and S Berres ldquoA Secure SteganographicAlgorithmBased on FrequencyDomain for the Transmission ofHidden Informationrdquo Security and Communication Networksvol 2017 pp 1ndash14 2017

[25] A Pradhan K Raja Sekhar and G Swain ldquoDigital imagesteganography based on seven way pixel value differencingrdquoIndian Journal of Science and Technology vol 9 no 37 ArticleID 88557 2016

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Mathematical Problems in Engineering

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AnalysisInternational Journal of

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

4 Mathematical Problems in Engineering

Table 3 Results of existing techniques

Images512 times 512 times 3

Wu and Tsai [5] Shen and Huang [23]PSNR Capacity 119876 BPB PSNR Capacity 119876 BPB

P4 P3 P2

P5 Pc P1

P6 P7 P8

(a)

pc

p4

p1

p2p

3

p5

p6 p

7 p8

(b)

plowastc plowast

1

plowast2plowast

3plowast4

plowast5

plowast6 plowast

7 plowast8

(c)

Figure 2 (a) Cover pixel block (b) stego block and (c) stego block used for extraction

value of the three LSBs of 11990110158408is 1199042 and the decimal value of

8using (4)

119896= 119901119896 + 119909

such that the condition (11990110158401015840119896mod 4 = 119898119896) satisfies Similarly

the condition (119901101584010158401015840119896

119896mod 4 = 119898119896) does

not satisfy then set 119901101584010158401015840119896= minus10 Now calculate 1199011015840

119896by (3) This

32 The Extraction Procedure

Step 2 The LSB bit of 119901lowast8is checked if it is 1 then for this

119888and next two LSBs

of 119901lowast8are extracted Furthermore the 119889lowast

119894= |119901lowast119888minus 119901lowast119894| and

119894

119894is converted to 119899119894 binary bits where 119899119894

Step 3 If the LSB bit of 119901lowast8is 0 then for this block the

extraction procedure of LSB + EMD is applied as follows

The next two LSBs of 119901lowast8are extracted For all the remaining

Mathematical Problems in Engineering 5

Table 4 Results of proposed technique 1

Images512 times 512 times 3

Table 5 Results of proposed technique 2

Images512 times 512 times 3

(a) Lena (b) Baboon (c) Boat (d) Pot

Figure 3 Original images

Figure 4 Stego images of technique 1 (Type 1)

6 Mathematical Problems in Engineering

Figure 5 Stego images of technique 1 (Type 2)

Figure 6 Stego images of technique 2 (Type 1)

Figure 7 Stego images of technique 2 (Type 2)

Table 6 Average results of proposed techniques

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

5 Conclusion

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 5

Table 4 Results of proposed technique 1

Images512 times 512 times 3

Table 5 Results of proposed technique 2

Images512 times 512 times 3

(a) Lena (b) Baboon (c) Boat (d) Pot

Figure 3 Original images

Figure 4 Stego images of technique 1 (Type 1)

6 Mathematical Problems in Engineering

Figure 5 Stego images of technique 1 (Type 2)

Figure 6 Stego images of technique 2 (Type 1)

Figure 7 Stego images of technique 2 (Type 2)

Table 6 Average results of proposed techniques

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

5 Conclusion

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

Figure 5 Stego images of technique 1 (Type 2)

Figure 6 Stego images of technique 2 (Type 1)

Figure 7 Stego images of technique 2 (Type 2)

Table 6 Average results of proposed techniques

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

5 Conclusion

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Shen and Huang

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(b) Shen and Huang

Figure 8 PDH analysis for Shen and Huangrsquos technique

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 3 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 3 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 3 PVD + 3 LSB + EMD (Type 2)

Figure 9 PDH analysis for proposed technique 1 (Type 1 and Type 2)

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

5 Conclusion

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(a) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Lena CoverLena Stego

times104

3

2

1

0

Occ

urre

nces

(b) Proposed 7 PVD + 3 LSB + EMD (Type 2)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(c) Proposed 7 PVD + 3 LSB + EMD (Type 1)

minus40 minus20 0 20 40

Pixel difference

Baboon CoverBaboon Stego

times104

3

2

1

0

Occ

urre

nces

(d) Proposed 7 PVD + 3 LSB + EMD (Type 2)

Figure 10 PDH analysis for proposed technique 2 (Type 1 and Type 2)

Table 7 Average results of Kieu and Changrsquos technique [19]

119878 value BPB PSNR2 1 52393 15 49894 2 46746 25 43298 3 408212 35 373116 4 348223 45 3169

5 Conclusion

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 9

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsingu

lar

pixe

l gro

ups

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 11 RS analysis for Proposed technique 1 (Type 1 and Type 2)

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

10 Mathematical Problems in Engineering

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(a) Lena (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(b) Baboon (Type 1)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(c) Lena (Type 2)

50

45

40

35

30

25

20

Perc

enta

ge o

f the

regu

lar a

ndsin

gula

rpix

el g

roup

s

0 20 40 60 80 100

Percentage of hiding capacity

Rm

Rminusm

SmSminusm

(d) Baboon (Type 2)

Figure 12 RS analysis of Proposed for proposed technique 2 (Type 1 and Type 2)

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

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